Final answer:
For the function f(x) = ax + q, the derivative is simply the coefficient a, since it represents the slope of the function, and the domain is all real numbers.
Step-by-step explanation:
The definition of derivative is used to find the rate at which a function is changing at any given point. For the linear function f(x) = ax + q, where a and q are constants, we can find the derivative using the limit definition of the derivative. However, because this is a linear function, its derivative can be found more directly, as the slope of the function is constant.
The derivative f'(x) is equal to a, since the slope of a line y = mx + b is m, and for our function, a corresponds to m. Therefore, f'(x) = a. The domain of the derivative is all real numbers because a linear function is differentiable everywhere on its domain, which is also all real numbers.